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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    package org.apache.commons.math3.optim.nonlinear.scalar.noderiv;<a name="line.17"></a>
<FONT color="green">018</FONT>    <a name="line.18"></a>
<FONT color="green">019</FONT>    import org.apache.commons.math3.util.FastMath;<a name="line.19"></a>
<FONT color="green">020</FONT>    import org.apache.commons.math3.util.MathArrays;<a name="line.20"></a>
<FONT color="green">021</FONT>    import org.apache.commons.math3.analysis.UnivariateFunction;<a name="line.21"></a>
<FONT color="green">022</FONT>    import org.apache.commons.math3.exception.NumberIsTooSmallException;<a name="line.22"></a>
<FONT color="green">023</FONT>    import org.apache.commons.math3.exception.NotStrictlyPositiveException;<a name="line.23"></a>
<FONT color="green">024</FONT>    import org.apache.commons.math3.optim.MaxEval;<a name="line.24"></a>
<FONT color="green">025</FONT>    import org.apache.commons.math3.optim.nonlinear.scalar.GoalType;<a name="line.25"></a>
<FONT color="green">026</FONT>    import org.apache.commons.math3.optim.PointValuePair;<a name="line.26"></a>
<FONT color="green">027</FONT>    import org.apache.commons.math3.optim.ConvergenceChecker;<a name="line.27"></a>
<FONT color="green">028</FONT>    import org.apache.commons.math3.optim.nonlinear.scalar.MultivariateOptimizer;<a name="line.28"></a>
<FONT color="green">029</FONT>    import org.apache.commons.math3.optim.univariate.BracketFinder;<a name="line.29"></a>
<FONT color="green">030</FONT>    import org.apache.commons.math3.optim.univariate.BrentOptimizer;<a name="line.30"></a>
<FONT color="green">031</FONT>    import org.apache.commons.math3.optim.univariate.UnivariatePointValuePair;<a name="line.31"></a>
<FONT color="green">032</FONT>    import org.apache.commons.math3.optim.univariate.SimpleUnivariateValueChecker;<a name="line.32"></a>
<FONT color="green">033</FONT>    import org.apache.commons.math3.optim.univariate.SearchInterval;<a name="line.33"></a>
<FONT color="green">034</FONT>    import org.apache.commons.math3.optim.univariate.UnivariateObjectiveFunction;<a name="line.34"></a>
<FONT color="green">035</FONT>    <a name="line.35"></a>
<FONT color="green">036</FONT>    /**<a name="line.36"></a>
<FONT color="green">037</FONT>     * Powell algorithm.<a name="line.37"></a>
<FONT color="green">038</FONT>     * This code is translated and adapted from the Python version of this<a name="line.38"></a>
<FONT color="green">039</FONT>     * algorithm (as implemented in module {@code optimize.py} v0.5 of<a name="line.39"></a>
<FONT color="green">040</FONT>     * &lt;em&gt;SciPy&lt;/em&gt;).<a name="line.40"></a>
<FONT color="green">041</FONT>     * &lt;br/&gt;<a name="line.41"></a>
<FONT color="green">042</FONT>     * The default stopping criterion is based on the differences of the<a name="line.42"></a>
<FONT color="green">043</FONT>     * function value between two successive iterations. It is however possible<a name="line.43"></a>
<FONT color="green">044</FONT>     * to define a custom convergence checker that might terminate the algorithm<a name="line.44"></a>
<FONT color="green">045</FONT>     * earlier.<a name="line.45"></a>
<FONT color="green">046</FONT>     * &lt;br/&gt;<a name="line.46"></a>
<FONT color="green">047</FONT>     * The internal line search optimizer is a {@link BrentOptimizer} with a<a name="line.47"></a>
<FONT color="green">048</FONT>     * convergence checker set to {@link SimpleUnivariateValueChecker}.<a name="line.48"></a>
<FONT color="green">049</FONT>     *<a name="line.49"></a>
<FONT color="green">050</FONT>     * @version $Id: PowellOptimizer.java 1413594 2012-11-26 13:16:39Z erans $<a name="line.50"></a>
<FONT color="green">051</FONT>     * @since 2.2<a name="line.51"></a>
<FONT color="green">052</FONT>     */<a name="line.52"></a>
<FONT color="green">053</FONT>    public class PowellOptimizer<a name="line.53"></a>
<FONT color="green">054</FONT>        extends MultivariateOptimizer {<a name="line.54"></a>
<FONT color="green">055</FONT>        /**<a name="line.55"></a>
<FONT color="green">056</FONT>         * Minimum relative tolerance.<a name="line.56"></a>
<FONT color="green">057</FONT>         */<a name="line.57"></a>
<FONT color="green">058</FONT>        private static final double MIN_RELATIVE_TOLERANCE = 2 * FastMath.ulp(1d);<a name="line.58"></a>
<FONT color="green">059</FONT>        /**<a name="line.59"></a>
<FONT color="green">060</FONT>         * Relative threshold.<a name="line.60"></a>
<FONT color="green">061</FONT>         */<a name="line.61"></a>
<FONT color="green">062</FONT>        private final double relativeThreshold;<a name="line.62"></a>
<FONT color="green">063</FONT>        /**<a name="line.63"></a>
<FONT color="green">064</FONT>         * Absolute threshold.<a name="line.64"></a>
<FONT color="green">065</FONT>         */<a name="line.65"></a>
<FONT color="green">066</FONT>        private final double absoluteThreshold;<a name="line.66"></a>
<FONT color="green">067</FONT>        /**<a name="line.67"></a>
<FONT color="green">068</FONT>         * Line search.<a name="line.68"></a>
<FONT color="green">069</FONT>         */<a name="line.69"></a>
<FONT color="green">070</FONT>        private final LineSearch line;<a name="line.70"></a>
<FONT color="green">071</FONT>    <a name="line.71"></a>
<FONT color="green">072</FONT>        /**<a name="line.72"></a>
<FONT color="green">073</FONT>         * This constructor allows to specify a user-defined convergence checker,<a name="line.73"></a>
<FONT color="green">074</FONT>         * in addition to the parameters that control the default convergence<a name="line.74"></a>
<FONT color="green">075</FONT>         * checking procedure.<a name="line.75"></a>
<FONT color="green">076</FONT>         * &lt;br/&gt;<a name="line.76"></a>
<FONT color="green">077</FONT>         * The internal line search tolerances are set to the square-root of their<a name="line.77"></a>
<FONT color="green">078</FONT>         * corresponding value in the multivariate optimizer.<a name="line.78"></a>
<FONT color="green">079</FONT>         *<a name="line.79"></a>
<FONT color="green">080</FONT>         * @param rel Relative threshold.<a name="line.80"></a>
<FONT color="green">081</FONT>         * @param abs Absolute threshold.<a name="line.81"></a>
<FONT color="green">082</FONT>         * @param checker Convergence checker.<a name="line.82"></a>
<FONT color="green">083</FONT>         * @throws NotStrictlyPositiveException if {@code abs &lt;= 0}.<a name="line.83"></a>
<FONT color="green">084</FONT>         * @throws NumberIsTooSmallException if {@code rel &lt; 2 * Math.ulp(1d)}.<a name="line.84"></a>
<FONT color="green">085</FONT>         */<a name="line.85"></a>
<FONT color="green">086</FONT>        public PowellOptimizer(double rel,<a name="line.86"></a>
<FONT color="green">087</FONT>                               double abs,<a name="line.87"></a>
<FONT color="green">088</FONT>                               ConvergenceChecker&lt;PointValuePair&gt; checker) {<a name="line.88"></a>
<FONT color="green">089</FONT>            this(rel, abs, FastMath.sqrt(rel), FastMath.sqrt(abs), checker);<a name="line.89"></a>
<FONT color="green">090</FONT>        }<a name="line.90"></a>
<FONT color="green">091</FONT>    <a name="line.91"></a>
<FONT color="green">092</FONT>        /**<a name="line.92"></a>
<FONT color="green">093</FONT>         * This constructor allows to specify a user-defined convergence checker,<a name="line.93"></a>
<FONT color="green">094</FONT>         * in addition to the parameters that control the default convergence<a name="line.94"></a>
<FONT color="green">095</FONT>         * checking procedure and the line search tolerances.<a name="line.95"></a>
<FONT color="green">096</FONT>         *<a name="line.96"></a>
<FONT color="green">097</FONT>         * @param rel Relative threshold for this optimizer.<a name="line.97"></a>
<FONT color="green">098</FONT>         * @param abs Absolute threshold for this optimizer.<a name="line.98"></a>
<FONT color="green">099</FONT>         * @param lineRel Relative threshold for the internal line search optimizer.<a name="line.99"></a>
<FONT color="green">100</FONT>         * @param lineAbs Absolute threshold for the internal line search optimizer.<a name="line.100"></a>
<FONT color="green">101</FONT>         * @param checker Convergence checker.<a name="line.101"></a>
<FONT color="green">102</FONT>         * @throws NotStrictlyPositiveException if {@code abs &lt;= 0}.<a name="line.102"></a>
<FONT color="green">103</FONT>         * @throws NumberIsTooSmallException if {@code rel &lt; 2 * Math.ulp(1d)}.<a name="line.103"></a>
<FONT color="green">104</FONT>         */<a name="line.104"></a>
<FONT color="green">105</FONT>        public PowellOptimizer(double rel,<a name="line.105"></a>
<FONT color="green">106</FONT>                               double abs,<a name="line.106"></a>
<FONT color="green">107</FONT>                               double lineRel,<a name="line.107"></a>
<FONT color="green">108</FONT>                               double lineAbs,<a name="line.108"></a>
<FONT color="green">109</FONT>                               ConvergenceChecker&lt;PointValuePair&gt; checker) {<a name="line.109"></a>
<FONT color="green">110</FONT>            super(checker);<a name="line.110"></a>
<FONT color="green">111</FONT>    <a name="line.111"></a>
<FONT color="green">112</FONT>            if (rel &lt; MIN_RELATIVE_TOLERANCE) {<a name="line.112"></a>
<FONT color="green">113</FONT>                throw new NumberIsTooSmallException(rel, MIN_RELATIVE_TOLERANCE, true);<a name="line.113"></a>
<FONT color="green">114</FONT>            }<a name="line.114"></a>
<FONT color="green">115</FONT>            if (abs &lt;= 0) {<a name="line.115"></a>
<FONT color="green">116</FONT>                throw new NotStrictlyPositiveException(abs);<a name="line.116"></a>
<FONT color="green">117</FONT>            }<a name="line.117"></a>
<FONT color="green">118</FONT>            relativeThreshold = rel;<a name="line.118"></a>
<FONT color="green">119</FONT>            absoluteThreshold = abs;<a name="line.119"></a>
<FONT color="green">120</FONT>    <a name="line.120"></a>
<FONT color="green">121</FONT>            // Create the line search optimizer.<a name="line.121"></a>
<FONT color="green">122</FONT>            line = new LineSearch(lineRel,<a name="line.122"></a>
<FONT color="green">123</FONT>                                  lineAbs);<a name="line.123"></a>
<FONT color="green">124</FONT>        }<a name="line.124"></a>
<FONT color="green">125</FONT>    <a name="line.125"></a>
<FONT color="green">126</FONT>        /**<a name="line.126"></a>
<FONT color="green">127</FONT>         * The parameters control the default convergence checking procedure.<a name="line.127"></a>
<FONT color="green">128</FONT>         * &lt;br/&gt;<a name="line.128"></a>
<FONT color="green">129</FONT>         * The internal line search tolerances are set to the square-root of their<a name="line.129"></a>
<FONT color="green">130</FONT>         * corresponding value in the multivariate optimizer.<a name="line.130"></a>
<FONT color="green">131</FONT>         *<a name="line.131"></a>
<FONT color="green">132</FONT>         * @param rel Relative threshold.<a name="line.132"></a>
<FONT color="green">133</FONT>         * @param abs Absolute threshold.<a name="line.133"></a>
<FONT color="green">134</FONT>         * @throws NotStrictlyPositiveException if {@code abs &lt;= 0}.<a name="line.134"></a>
<FONT color="green">135</FONT>         * @throws NumberIsTooSmallException if {@code rel &lt; 2 * Math.ulp(1d)}.<a name="line.135"></a>
<FONT color="green">136</FONT>         */<a name="line.136"></a>
<FONT color="green">137</FONT>        public PowellOptimizer(double rel,<a name="line.137"></a>
<FONT color="green">138</FONT>                               double abs) {<a name="line.138"></a>
<FONT color="green">139</FONT>            this(rel, abs, null);<a name="line.139"></a>
<FONT color="green">140</FONT>        }<a name="line.140"></a>
<FONT color="green">141</FONT>    <a name="line.141"></a>
<FONT color="green">142</FONT>        /**<a name="line.142"></a>
<FONT color="green">143</FONT>         * Builds an instance with the default convergence checking procedure.<a name="line.143"></a>
<FONT color="green">144</FONT>         *<a name="line.144"></a>
<FONT color="green">145</FONT>         * @param rel Relative threshold.<a name="line.145"></a>
<FONT color="green">146</FONT>         * @param abs Absolute threshold.<a name="line.146"></a>
<FONT color="green">147</FONT>         * @param lineRel Relative threshold for the internal line search optimizer.<a name="line.147"></a>
<FONT color="green">148</FONT>         * @param lineAbs Absolute threshold for the internal line search optimizer.<a name="line.148"></a>
<FONT color="green">149</FONT>         * @throws NotStrictlyPositiveException if {@code abs &lt;= 0}.<a name="line.149"></a>
<FONT color="green">150</FONT>         * @throws NumberIsTooSmallException if {@code rel &lt; 2 * Math.ulp(1d)}.<a name="line.150"></a>
<FONT color="green">151</FONT>         */<a name="line.151"></a>
<FONT color="green">152</FONT>        public PowellOptimizer(double rel,<a name="line.152"></a>
<FONT color="green">153</FONT>                               double abs,<a name="line.153"></a>
<FONT color="green">154</FONT>                               double lineRel,<a name="line.154"></a>
<FONT color="green">155</FONT>                               double lineAbs) {<a name="line.155"></a>
<FONT color="green">156</FONT>            this(rel, abs, lineRel, lineAbs, null);<a name="line.156"></a>
<FONT color="green">157</FONT>        }<a name="line.157"></a>
<FONT color="green">158</FONT>    <a name="line.158"></a>
<FONT color="green">159</FONT>        /** {@inheritDoc} */<a name="line.159"></a>
<FONT color="green">160</FONT>        @Override<a name="line.160"></a>
<FONT color="green">161</FONT>        protected PointValuePair doOptimize() {<a name="line.161"></a>
<FONT color="green">162</FONT>            final GoalType goal = getGoalType();<a name="line.162"></a>
<FONT color="green">163</FONT>            final double[] guess = getStartPoint();<a name="line.163"></a>
<FONT color="green">164</FONT>            final int n = guess.length;<a name="line.164"></a>
<FONT color="green">165</FONT>    <a name="line.165"></a>
<FONT color="green">166</FONT>            final double[][] direc = new double[n][n];<a name="line.166"></a>
<FONT color="green">167</FONT>            for (int i = 0; i &lt; n; i++) {<a name="line.167"></a>
<FONT color="green">168</FONT>                direc[i][i] = 1;<a name="line.168"></a>
<FONT color="green">169</FONT>            }<a name="line.169"></a>
<FONT color="green">170</FONT>    <a name="line.170"></a>
<FONT color="green">171</FONT>            final ConvergenceChecker&lt;PointValuePair&gt; checker<a name="line.171"></a>
<FONT color="green">172</FONT>                = getConvergenceChecker();<a name="line.172"></a>
<FONT color="green">173</FONT>    <a name="line.173"></a>
<FONT color="green">174</FONT>            double[] x = guess;<a name="line.174"></a>
<FONT color="green">175</FONT>            double fVal = computeObjectiveValue(x);<a name="line.175"></a>
<FONT color="green">176</FONT>            double[] x1 = x.clone();<a name="line.176"></a>
<FONT color="green">177</FONT>            int iter = 0;<a name="line.177"></a>
<FONT color="green">178</FONT>            while (true) {<a name="line.178"></a>
<FONT color="green">179</FONT>                ++iter;<a name="line.179"></a>
<FONT color="green">180</FONT>    <a name="line.180"></a>
<FONT color="green">181</FONT>                double fX = fVal;<a name="line.181"></a>
<FONT color="green">182</FONT>                double fX2 = 0;<a name="line.182"></a>
<FONT color="green">183</FONT>                double delta = 0;<a name="line.183"></a>
<FONT color="green">184</FONT>                int bigInd = 0;<a name="line.184"></a>
<FONT color="green">185</FONT>                double alphaMin = 0;<a name="line.185"></a>
<FONT color="green">186</FONT>    <a name="line.186"></a>
<FONT color="green">187</FONT>                for (int i = 0; i &lt; n; i++) {<a name="line.187"></a>
<FONT color="green">188</FONT>                    final double[] d = MathArrays.copyOf(direc[i]);<a name="line.188"></a>
<FONT color="green">189</FONT>    <a name="line.189"></a>
<FONT color="green">190</FONT>                    fX2 = fVal;<a name="line.190"></a>
<FONT color="green">191</FONT>    <a name="line.191"></a>
<FONT color="green">192</FONT>                    final UnivariatePointValuePair optimum = line.search(x, d);<a name="line.192"></a>
<FONT color="green">193</FONT>                    fVal = optimum.getValue();<a name="line.193"></a>
<FONT color="green">194</FONT>                    alphaMin = optimum.getPoint();<a name="line.194"></a>
<FONT color="green">195</FONT>                    final double[][] result = newPointAndDirection(x, d, alphaMin);<a name="line.195"></a>
<FONT color="green">196</FONT>                    x = result[0];<a name="line.196"></a>
<FONT color="green">197</FONT>    <a name="line.197"></a>
<FONT color="green">198</FONT>                    if ((fX2 - fVal) &gt; delta) {<a name="line.198"></a>
<FONT color="green">199</FONT>                        delta = fX2 - fVal;<a name="line.199"></a>
<FONT color="green">200</FONT>                        bigInd = i;<a name="line.200"></a>
<FONT color="green">201</FONT>                    }<a name="line.201"></a>
<FONT color="green">202</FONT>                }<a name="line.202"></a>
<FONT color="green">203</FONT>    <a name="line.203"></a>
<FONT color="green">204</FONT>                // Default convergence check.<a name="line.204"></a>
<FONT color="green">205</FONT>                boolean stop = 2 * (fX - fVal) &lt;=<a name="line.205"></a>
<FONT color="green">206</FONT>                    (relativeThreshold * (FastMath.abs(fX) + FastMath.abs(fVal)) +<a name="line.206"></a>
<FONT color="green">207</FONT>                     absoluteThreshold);<a name="line.207"></a>
<FONT color="green">208</FONT>    <a name="line.208"></a>
<FONT color="green">209</FONT>                final PointValuePair previous = new PointValuePair(x1, fX);<a name="line.209"></a>
<FONT color="green">210</FONT>                final PointValuePair current = new PointValuePair(x, fVal);<a name="line.210"></a>
<FONT color="green">211</FONT>                if (!stop) { // User-defined stopping criteria.<a name="line.211"></a>
<FONT color="green">212</FONT>                    if (checker != null) {<a name="line.212"></a>
<FONT color="green">213</FONT>                        stop = checker.converged(iter, previous, current);<a name="line.213"></a>
<FONT color="green">214</FONT>                    }<a name="line.214"></a>
<FONT color="green">215</FONT>                }<a name="line.215"></a>
<FONT color="green">216</FONT>                if (stop) {<a name="line.216"></a>
<FONT color="green">217</FONT>                    if (goal == GoalType.MINIMIZE) {<a name="line.217"></a>
<FONT color="green">218</FONT>                        return (fVal &lt; fX) ? current : previous;<a name="line.218"></a>
<FONT color="green">219</FONT>                    } else {<a name="line.219"></a>
<FONT color="green">220</FONT>                        return (fVal &gt; fX) ? current : previous;<a name="line.220"></a>
<FONT color="green">221</FONT>                    }<a name="line.221"></a>
<FONT color="green">222</FONT>                }<a name="line.222"></a>
<FONT color="green">223</FONT>    <a name="line.223"></a>
<FONT color="green">224</FONT>                final double[] d = new double[n];<a name="line.224"></a>
<FONT color="green">225</FONT>                final double[] x2 = new double[n];<a name="line.225"></a>
<FONT color="green">226</FONT>                for (int i = 0; i &lt; n; i++) {<a name="line.226"></a>
<FONT color="green">227</FONT>                    d[i] = x[i] - x1[i];<a name="line.227"></a>
<FONT color="green">228</FONT>                    x2[i] = 2 * x[i] - x1[i];<a name="line.228"></a>
<FONT color="green">229</FONT>                }<a name="line.229"></a>
<FONT color="green">230</FONT>    <a name="line.230"></a>
<FONT color="green">231</FONT>                x1 = x.clone();<a name="line.231"></a>
<FONT color="green">232</FONT>                fX2 = computeObjectiveValue(x2);<a name="line.232"></a>
<FONT color="green">233</FONT>    <a name="line.233"></a>
<FONT color="green">234</FONT>                if (fX &gt; fX2) {<a name="line.234"></a>
<FONT color="green">235</FONT>                    double t = 2 * (fX + fX2 - 2 * fVal);<a name="line.235"></a>
<FONT color="green">236</FONT>                    double temp = fX - fVal - delta;<a name="line.236"></a>
<FONT color="green">237</FONT>                    t *= temp * temp;<a name="line.237"></a>
<FONT color="green">238</FONT>                    temp = fX - fX2;<a name="line.238"></a>
<FONT color="green">239</FONT>                    t -= delta * temp * temp;<a name="line.239"></a>
<FONT color="green">240</FONT>    <a name="line.240"></a>
<FONT color="green">241</FONT>                    if (t &lt; 0.0) {<a name="line.241"></a>
<FONT color="green">242</FONT>                        final UnivariatePointValuePair optimum = line.search(x, d);<a name="line.242"></a>
<FONT color="green">243</FONT>                        fVal = optimum.getValue();<a name="line.243"></a>
<FONT color="green">244</FONT>                        alphaMin = optimum.getPoint();<a name="line.244"></a>
<FONT color="green">245</FONT>                        final double[][] result = newPointAndDirection(x, d, alphaMin);<a name="line.245"></a>
<FONT color="green">246</FONT>                        x = result[0];<a name="line.246"></a>
<FONT color="green">247</FONT>    <a name="line.247"></a>
<FONT color="green">248</FONT>                        final int lastInd = n - 1;<a name="line.248"></a>
<FONT color="green">249</FONT>                        direc[bigInd] = direc[lastInd];<a name="line.249"></a>
<FONT color="green">250</FONT>                        direc[lastInd] = result[1];<a name="line.250"></a>
<FONT color="green">251</FONT>                    }<a name="line.251"></a>
<FONT color="green">252</FONT>                }<a name="line.252"></a>
<FONT color="green">253</FONT>            }<a name="line.253"></a>
<FONT color="green">254</FONT>        }<a name="line.254"></a>
<FONT color="green">255</FONT>    <a name="line.255"></a>
<FONT color="green">256</FONT>        /**<a name="line.256"></a>
<FONT color="green">257</FONT>         * Compute a new point (in the original space) and a new direction<a name="line.257"></a>
<FONT color="green">258</FONT>         * vector, resulting from the line search.<a name="line.258"></a>
<FONT color="green">259</FONT>         *<a name="line.259"></a>
<FONT color="green">260</FONT>         * @param p Point used in the line search.<a name="line.260"></a>
<FONT color="green">261</FONT>         * @param d Direction used in the line search.<a name="line.261"></a>
<FONT color="green">262</FONT>         * @param optimum Optimum found by the line search.<a name="line.262"></a>
<FONT color="green">263</FONT>         * @return a 2-element array containing the new point (at index 0) and<a name="line.263"></a>
<FONT color="green">264</FONT>         * the new direction (at index 1).<a name="line.264"></a>
<FONT color="green">265</FONT>         */<a name="line.265"></a>
<FONT color="green">266</FONT>        private double[][] newPointAndDirection(double[] p,<a name="line.266"></a>
<FONT color="green">267</FONT>                                                double[] d,<a name="line.267"></a>
<FONT color="green">268</FONT>                                                double optimum) {<a name="line.268"></a>
<FONT color="green">269</FONT>            final int n = p.length;<a name="line.269"></a>
<FONT color="green">270</FONT>            final double[] nP = new double[n];<a name="line.270"></a>
<FONT color="green">271</FONT>            final double[] nD = new double[n];<a name="line.271"></a>
<FONT color="green">272</FONT>            for (int i = 0; i &lt; n; i++) {<a name="line.272"></a>
<FONT color="green">273</FONT>                nD[i] = d[i] * optimum;<a name="line.273"></a>
<FONT color="green">274</FONT>                nP[i] = p[i] + nD[i];<a name="line.274"></a>
<FONT color="green">275</FONT>            }<a name="line.275"></a>
<FONT color="green">276</FONT>    <a name="line.276"></a>
<FONT color="green">277</FONT>            final double[][] result = new double[2][];<a name="line.277"></a>
<FONT color="green">278</FONT>            result[0] = nP;<a name="line.278"></a>
<FONT color="green">279</FONT>            result[1] = nD;<a name="line.279"></a>
<FONT color="green">280</FONT>    <a name="line.280"></a>
<FONT color="green">281</FONT>            return result;<a name="line.281"></a>
<FONT color="green">282</FONT>        }<a name="line.282"></a>
<FONT color="green">283</FONT>    <a name="line.283"></a>
<FONT color="green">284</FONT>        /**<a name="line.284"></a>
<FONT color="green">285</FONT>         * Class for finding the minimum of the objective function along a given<a name="line.285"></a>
<FONT color="green">286</FONT>         * direction.<a name="line.286"></a>
<FONT color="green">287</FONT>         */<a name="line.287"></a>
<FONT color="green">288</FONT>        private class LineSearch extends BrentOptimizer {<a name="line.288"></a>
<FONT color="green">289</FONT>            /**<a name="line.289"></a>
<FONT color="green">290</FONT>             * Value that will pass the precondition check for {@link BrentOptimizer}<a name="line.290"></a>
<FONT color="green">291</FONT>             * but will not pass the convergence check, so that the custom checker<a name="line.291"></a>
<FONT color="green">292</FONT>             * will always decide when to stop the line search.<a name="line.292"></a>
<FONT color="green">293</FONT>             */<a name="line.293"></a>
<FONT color="green">294</FONT>            private static final double REL_TOL_UNUSED = 1e-15;<a name="line.294"></a>
<FONT color="green">295</FONT>            /**<a name="line.295"></a>
<FONT color="green">296</FONT>             * Value that will pass the precondition check for {@link BrentOptimizer}<a name="line.296"></a>
<FONT color="green">297</FONT>             * but will not pass the convergence check, so that the custom checker<a name="line.297"></a>
<FONT color="green">298</FONT>             * will always decide when to stop the line search.<a name="line.298"></a>
<FONT color="green">299</FONT>             */<a name="line.299"></a>
<FONT color="green">300</FONT>            private static final double ABS_TOL_UNUSED = Double.MIN_VALUE;<a name="line.300"></a>
<FONT color="green">301</FONT>            /**<a name="line.301"></a>
<FONT color="green">302</FONT>             * Automatic bracketing.<a name="line.302"></a>
<FONT color="green">303</FONT>             */<a name="line.303"></a>
<FONT color="green">304</FONT>            private final BracketFinder bracket = new BracketFinder();<a name="line.304"></a>
<FONT color="green">305</FONT>    <a name="line.305"></a>
<FONT color="green">306</FONT>            /**<a name="line.306"></a>
<FONT color="green">307</FONT>             * The "BrentOptimizer" default stopping criterion uses the tolerances<a name="line.307"></a>
<FONT color="green">308</FONT>             * to check the domain (point) values, not the function values.<a name="line.308"></a>
<FONT color="green">309</FONT>             * We thus create a custom checker to use function values.<a name="line.309"></a>
<FONT color="green">310</FONT>             *<a name="line.310"></a>
<FONT color="green">311</FONT>             * @param rel Relative threshold.<a name="line.311"></a>
<FONT color="green">312</FONT>             * @param abs Absolute threshold.<a name="line.312"></a>
<FONT color="green">313</FONT>             */<a name="line.313"></a>
<FONT color="green">314</FONT>            LineSearch(double rel,<a name="line.314"></a>
<FONT color="green">315</FONT>                       double abs) {<a name="line.315"></a>
<FONT color="green">316</FONT>                super(REL_TOL_UNUSED,<a name="line.316"></a>
<FONT color="green">317</FONT>                      ABS_TOL_UNUSED,<a name="line.317"></a>
<FONT color="green">318</FONT>                      new SimpleUnivariateValueChecker(rel, abs));<a name="line.318"></a>
<FONT color="green">319</FONT>            }<a name="line.319"></a>
<FONT color="green">320</FONT>    <a name="line.320"></a>
<FONT color="green">321</FONT>            /**<a name="line.321"></a>
<FONT color="green">322</FONT>             * Find the minimum of the function {@code f(p + alpha * d)}.<a name="line.322"></a>
<FONT color="green">323</FONT>             *<a name="line.323"></a>
<FONT color="green">324</FONT>             * @param p Starting point.<a name="line.324"></a>
<FONT color="green">325</FONT>             * @param d Search direction.<a name="line.325"></a>
<FONT color="green">326</FONT>             * @return the optimum.<a name="line.326"></a>
<FONT color="green">327</FONT>             * @throws org.apache.commons.math3.exception.TooManyEvaluationsException<a name="line.327"></a>
<FONT color="green">328</FONT>             * if the number of evaluations is exceeded.<a name="line.328"></a>
<FONT color="green">329</FONT>             */<a name="line.329"></a>
<FONT color="green">330</FONT>            public UnivariatePointValuePair search(final double[] p, final double[] d) {<a name="line.330"></a>
<FONT color="green">331</FONT>                final int n = p.length;<a name="line.331"></a>
<FONT color="green">332</FONT>                final UnivariateFunction f = new UnivariateFunction() {<a name="line.332"></a>
<FONT color="green">333</FONT>                        public double value(double alpha) {<a name="line.333"></a>
<FONT color="green">334</FONT>                            final double[] x = new double[n];<a name="line.334"></a>
<FONT color="green">335</FONT>                            for (int i = 0; i &lt; n; i++) {<a name="line.335"></a>
<FONT color="green">336</FONT>                                x[i] = p[i] + alpha * d[i];<a name="line.336"></a>
<FONT color="green">337</FONT>                            }<a name="line.337"></a>
<FONT color="green">338</FONT>                            final double obj = PowellOptimizer.this.computeObjectiveValue(x);<a name="line.338"></a>
<FONT color="green">339</FONT>                            return obj;<a name="line.339"></a>
<FONT color="green">340</FONT>                        }<a name="line.340"></a>
<FONT color="green">341</FONT>                    };<a name="line.341"></a>
<FONT color="green">342</FONT>    <a name="line.342"></a>
<FONT color="green">343</FONT>                final GoalType goal = PowellOptimizer.this.getGoalType();<a name="line.343"></a>
<FONT color="green">344</FONT>                bracket.search(f, goal, 0, 1);<a name="line.344"></a>
<FONT color="green">345</FONT>                // Passing "MAX_VALUE" as a dummy value because it is the enclosing<a name="line.345"></a>
<FONT color="green">346</FONT>                // class that counts the number of evaluations (and will eventually<a name="line.346"></a>
<FONT color="green">347</FONT>                // generate the exception).<a name="line.347"></a>
<FONT color="green">348</FONT>                return optimize(new MaxEval(Integer.MAX_VALUE),<a name="line.348"></a>
<FONT color="green">349</FONT>                                new UnivariateObjectiveFunction(f),<a name="line.349"></a>
<FONT color="green">350</FONT>                                goal,<a name="line.350"></a>
<FONT color="green">351</FONT>                                new SearchInterval(bracket.getLo(),<a name="line.351"></a>
<FONT color="green">352</FONT>                                                   bracket.getHi(),<a name="line.352"></a>
<FONT color="green">353</FONT>                                                   bracket.getMid()));<a name="line.353"></a>
<FONT color="green">354</FONT>            }<a name="line.354"></a>
<FONT color="green">355</FONT>        }<a name="line.355"></a>
<FONT color="green">356</FONT>    }<a name="line.356"></a>




























































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